In November, 2011, the Financial Stability Board, in collaboration with the International Monetary Fund, published a list of 29 “systemically important financial institutions” (SIFIs). This designation reflects a concern that the failure of any one of them could have dramatic negative consequences for the global economy and is based on “their size, complexity, and systemic interconnectedness”. While the characteristics of “size” and “systemic interconnectedness” have been the subject of a good deal of quantitative analysis, less attention has been paid to measures of a firm’s “complexity.” In this paper we take on the challenges of measuring the complexity of a financial institution by exploring the use of the structure of an individual firm’s control hierarchy as a proxy for institutional complexity. The control hierarchy is a network representation of the institution and its subsidiaries. We show that this mathematical representation (and various associated metrics) provides a consistent way to compare the complexity of firms with often very disparate business models and as such may provide the foundation for determining a SIFI designation. By quantifying the level of complexity of a firm, our approach also may prove useful should firms need to reduce their level of complexity either in response to business or regulatory needs. Using a data set containing the control hierarchies of many of the designated SIFIs, we find that between 2011 and 2013, these firms have decreased their level of complexity, perhaps in response to regulatory requirements.

The Intrafirm Complexity Of Systemically Important Financial Institutions – Introduction

The Financial Stability Board (FSB) describes a systemically important financial institution, or SIFI, as a financial institution “whose disorderly failure, because of their size, complexity and systemic interconnectedness, would cause significant disruption to the wider financial system and economic activity.”1 Developed in the aftermath of the recent global financial crisis, this characterization represents an expanded regulatory definition relative to earlier ones based primarily on size (e.g., the list of “mandatory banks” subject to the Basel II capital regulations, see 72 FR 69298, December 7, 2007).

In particular, the collapse of Lehman Brothers in September 2008 highlighted the extensive interconnectedness of the financial system and the importance of considering not just the risk of a single firm but the risk to the entire financial system, i.e., the systemic risk. Interconnectedness can be formulated mathematically in terms of networks and indeed, a May 10, 2013 speech by Fed Chairman Ben Bernanke noted that “Network analysis, yet another promising tool under active development, has the potential to help us better monitor the interconnectedness of financial institutions and markets.” In fact, there are a number of studies applying the techniques and metrics of network science to the analysis of economic and financial networks (e.g., Hutchinson et al., 1994, Cohen-Cole et al., 2010, Haldane and May 2011, Adamic et al., 2012, Battiston et al., 2012, Hautsch et al., 2012, 2013, Squartini et al., 2013, Caccioli et al., 2014). These papers have shown that the network of interdependencies is complex, and dependences of many different types overlap and interact (May, Levin, and Sugihara 2008). Because financial institutions hold various levels of interest in one another (Vitali et al., 2011), the collapse of any single entity can initiate a cascade of unforeseen events that in the worst of cases brings about the failures of many other financial participants, be they individuals, institutions, or even sovereign nations (Foti, et al., 2013).

While the interrelationships among financial network participants now are being widely studied, there has been comparatively little development of metrics concerning the complexity of the individual firms that comprise the system – the other key attribute highlighted in the Systemically Important Financial Institutions definition. Failing any direct definition, one view of an individual firm’s complexity comes from the lens of governance: “high complexity” would be interpreted as a corporate control structure rife with governance challenges for a firm’s management, resulting in a lack of oversight that in turn poses significant operational, reputational, and balance sheet risk (Vitali et al., 2011). For example supervisory challenges have been evident in news surrounding both JPMorgan’s large trading loss and Barclays’s LIBOR fine, with senior management at both firms denying knowledge of the underlying operational lapses. A similar “rogue trader” event occurred at Société Générale in July 2007 and threatened to disrupt financial markets before it was determined to be an isolated incident. These examples illustrate the challenges associated with assuring sufficient oversight in organizations that often have very complex control and governance structures. Such complexity contributes to the possibility that subsidiaries act in relative obscurity within the organization, in spite of their significance to the overall viability of the parent institution. In this context, complexity therefore poses risk to the organization. When coupled with a high degree of interconnectivity, the combination can pose a risk to the global financial system as a whole.